If f(x) = (ax^2 + b)^3, then the function g such that f(g(x)) = g… - Vidyadip

MCQ

If $f\text{(x)} = \text{(ax^2 + b)}^3,$ then the function $g$ such that $f(g\text{(x)}) = \text{g(f(x))}$ is given by:

A
$\text{g}(\text{x})=\Big(\frac{\text{b}-\text{x}^\frac{1}{3}}{\text{a}}\Big)$
B
$\text{g}(\text{x})=\frac{1}{(\text{ax}^2+\text{b})^3}$
C
$\text{g}(\text{x})=(\text{ax}^2+\text{b})^\frac{1}{3}$
✓
$\text{g}(\text{x})=\Big(\frac{\text{x}^\frac{1}{3}-\text{b}}{\text{a}}\Big)^\frac{1}{2}$

✓

Answer

Correct option: D.

$\text{g}(\text{x})=\Big(\frac{\text{x}^\frac{1}{3}-\text{b}}{\text{a}}\Big)^\frac{1}{2}$

$\text{g}(\text{x})=\Big(\frac{\text{x}^\frac{1}{3}-\text{b}}{\text{a}}\Big)^\frac{1}{2}$

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